It is known in the art that increasing the amount of data that can be transmitted or stored over a given time, referred to as density of data, provides the advantages of reducing the cost and time associated with transmitting and storing data. Because of these advantages, it has long been a goal in the electronics industry to increase the density of data that is transmitted or stored. To this end, many systems use run-length limited (RLL) coding and peak detection (PD) techniques to achieve high reliability of data transmission and storage at high densities. An even better increase in density can be realized through the use of more advantaged techniques such as partial response (PR) signaling and maximum-likelihood (ML) methodology, or a combination of the two. For instance, today's disk drive read/write channels make use of the Partial Response Maximum Likelihood (PR ML) method in order to retrieve information from magnetic media, such as a disc drive.
PR signaling is a synchronous detection scheme in which each pulse contains more than one non-zero sample such that each sample contains just part of the pulse. ML uses the sequence of received read samples to determine the actual data sequence and user data. While PR signaling is a technique that enforces spectral properties and allows a controlled amount of intersymbol interference. ML sequence estimation, particularly with the Viterbi algorithm, improves the detection of symbol sequences in the presence of intersymbol interference. ML sequence estimation allows most PR schemes to perform practically in a system with errors caused by intersymbol interference. Usually the ML operation is performed by a detector, such as the Viterbi Detector (VD) that uses the Viterbi algorithm to determine which sequence, of all possible data sequences, is the sequence most like the actual data sequence as determined by the minimum square error.
Viterbi detection uses a recursive technique called dynamic programming that was originally used to find a solution to the classical shortest path problem, but has been tailored to data detection. The recursive nature of dynamic programming causes the total processing effort to grow only linearly with the message length of data, as opposed to non-linear growth. The Viterbi algorithm is used to find the "most likely" path through the trellis diagram. The trellis diagram is determined by the modulation code and the memory length of the system. The maximum-likelihood data sequence is a path through this diagram. The trellis describing the noiseless output sequences for a channel equalized to EE . . . EPR4=E.sup.m PR4 (m=1, 2, 3, . . . ) has 2.sup.(m+2) states. For m=0, in the case of PR4, two trellises with two states each can be used. These two states represent the number of states required of a Viterbi detector assuming additive white Gaussian noise; a Viterbi detector for correlated Gaussian noise would require many more states. A detailed treatment of the subject of Viterbi Detection can be found by reference to Chapter 7 of Jan W. M. Bergmans book entitled "Digital Baseband Transmission and Recording," published in 1996 by Kluwer Academic Publishers, which is herein incorporated by reference.
PR signaling also allows a better handling of intersymbol interference and a more efficient utilization of the bandwidth of a given channel. Because the intersymbol interference is known to be present, the receiver can take it into account. PR signaling in communications allows transmissions at the Nyquist rate, and provides a favorable trade-off between error probability and the available spectrum. The PR systems described by the polynomials (1+D), (1-D), and (1-D).sup.2 are called duobinary, dicode, and class-IV, respectively, where D represents one bit cell delay and D.sup.2 represents two bit cell delays of the channel. D=e.sup.-j.omega.t, where .omega. is a frequency variable in radians per second and t is the sampling time interval in seconds.
Conventional disc drives are used to record and retrieve information. As discs become more prevalent as the medium of choice for storing information in both computer and home entertainment systems and equipment, disk drives likewise become more prevalent and important components of such systems. PR and ML have been used in communications signaling for years, and have now been applied commercially within magnetic hard disk drives. The PR that is today commonly used to recover information from a disk drive or other magnetic media is class-IV (PR4); it is a preferred partial response system in disc drives, since there is a close correlation between the idealized PR4 spectrum and the natural characteristics of a magnetic data write/read channel. Application of the Viterbi algorithm to PR4 data streams within a magnetic recording channel is known to improve detection of original symbol sequences in the presence of intersymbol interference and also to improve signal to noise ratio (SNR) over comparable peak detection techniques.
PR4 is demonstrated by the following equation: (1-D)(1+D).sup.n, where n is the degree of the (1+D) polynomial and D is the delay element, as described above. Of course, the class of PR is defined by the degree of the polynomial; thus, n=1 defines PR4, n=2 defines EPR4, and n=3 defines EEPR4, or simply E.sup.n-1 PR4. EPR4 and EEPR4 are higher order PR detection schemes that further increase the density of data that can be stored and transmitted. The PR4 magnitude response, 1-D.sup.2, emphasizes midband frequencies and results in a read channel with increased immunity to noise and distortion at both low and high frequencies.
Because of the channel properties of current disc drives or other magnetic or storage media, the read-back operation from a drive can be modeled as a 1-D process, meaning that the signal at the input of the read/write channel is different from zero only when a transition in the magnetization of the channel occurs. Thus, the (1+D).sup.n coefficient of PR4 actually represents the low-pass nature of the read channel itself. The whole channel model can therefore be considered to be the PR4 response convolved with written data, i.e.: Read(D)=(1-D)(1+D).sup.n Written(D). This target equation is representative of the ideal response of the channel that would allow for perfect data reconstruction and thus the equation to which it would be desirable to have the input signal to the channel matched to. The VD that performs the ML operation is therefore designed with this target equation in mind. The target equations for various classes of PR, including PR4, are demonstrated in FIG. 1.
As recording densities in the industry increase, it is proven that a higher order PR is needed to better match actual channel response to the ideal channel response. Unfortunately, higher order PR schemes, such as EPR4 and EEPR4 require more complex calculations, meaning less speed and more power, and more circuitry area in the VD. Additionally, a better quality head of the channel and magnetic media are often required to raise the SNR to a desired level.
In light of the foregoing, there is an unmet need in the art to be able to increase the maximum speed of the channel as much as possible so as to realize corresponding increases in the density of data that is transmitted or stored. This would preferably be accomplished without resorting to the use of higher order PR signaling with its attendant problems.